Optimal defined contribution pension management with salary and risky assets following jump diffusion processes

Abstract

The paper considers an optimal asset allocation problem for a defined contribution pension plan during the accumulation phase. The salary follows a stochastic process, which combines a compound Poisson jump with Brownian uncertainty. The plan aims to minimise the quadratic loss function over finite time horizon by investing in the market of risky assets and bank account. The risky assets are subjected to Poisson jump and Brownian motion. The closed-form optimal investment decision is derived from the corresponding Hamilton-Jacobi-Bellman equation.